Evolution Systems of Measures for Non-autonomous Ornstein-Uhlenbeck Processes with L\'evy noise

TL;DR

This paper investigates the existence, uniqueness, and explicit forms of evolution systems of measures for non-autonomous Ornstein-Uhlenbeck processes driven by Lévy noise, including concrete density computations.

Contribution

It provides new results on existence, uniqueness, and explicit density formulas for measures associated with non-autonomous Ornstein-Uhlenbeck processes with jumps.

Findings

Existence and uniqueness conditions established.

Explicit density formulas derived for specific cases.

Examples illustrating the measure computations provided.

Abstract

We examine the question of existence and uniqueness of evolution systems of measures for non-autonomous Ornstein-Uhlenbeck-type processes with jumps. In particular, we give examples where we explicitly compute the densities of such families of measures.